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HARVARD PHYS 11b - Homework #6

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Homework #6 Physics 11b Morii 3/17/2005 Due 3/25/2005, 4 PM in mailboxes outside Science Center 109 Read: Chapters 31, 32 Instructions: Please box your solutions. The homework problems are graded out of 3 points, and then the total re-scaled to 30. For each problem, in order to get full credit, you must also include a sentence explaining the most important idea you used in order to solve it. Do not summarize the whole solution, simply the one most important idea. HW Problems 1. Serway & Jewett 29.20 A current of 17.0 mA is maintained in a single circular loop of 2.00 m circumference. A magnetic field of 0.800 T is directed parallel to the plane of the loop. (a) Calculate the magnetic moment of the loop. (b) What is the magnitude of the torque exerted by the magnetic field on the loop? 2. Serway & Jewett 29.49 A flat copper ribbon 0.330 mm thick carries a steady current of 50.0 A and is located in a uniform 1.30-T magnetic field directed perpendicular to the plane of the ribbon. If a Hall voltage of 9.60 µV is measured across the ribbon, what is the charge density of the free electrons? What effective number of free electrons per atom does this result indicate? 3. Serway & Jewett 30.6 A conductor consists of a circular loop of radius R and two straight, long sections, as shown in the figure. The wire lies in the plane of the paper and carries a current I. Find an expression for the vector magnetic field at the center of the loop. (The straight sections are infinitely long.) 4. Serway & Jewett 30.9 Two very long, straight, parallel wires carry currents that are directed perpendicular to the page, as in the figure below. Wire 1 carries a current I1 into the page (in the –z direction) and passes through the x axis at x = +a. Wire 2 passes through the x axis at x = –2a and carries an unknown current I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 2µ0I1/(2πa). The current I2 can have either of two possible values. (a) Find the value of I2 with the smaller magnitude, stating it in terms of I1 and giving its direction. (b) Find the other possible value of I2.5. Serway & Jewett 30.13 A wire carrying a current I is bent into the shape of an equilateral triangle of side L. (a) Find the magnitude of the magnetic field at the center of the triangle. (b) At a point halfway between the center and any vertex, is the field stronger or weaker than at the center? 6. Serway & Jewett 30.19 Three long wires (wire 1, wire 2, and wire 3) hang vertically. The distance between wire 1 and wire 2 is 20.0 cm. On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 4.00 A. Wire 3 is located such that when it carries a certain current, each wire experiences no net force. Find (a) the position of wire 3, and (b) the magnitude and direction of the current in wire 3.7. Serway & Jewett 30.23 The figure below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, which is surrounded by an outer conductor, which is surrounded by another rubber layer. In a particular application, the current in the inner conductor is 1.00 A out of the page and the current in the outer conductor is 3.00 A into the page. Determine the magnitude and direction of the magnetic field at points a and b. 8. Serway & Jewett 30.28 Niobium metal becomes a superconductor when cooled below 9 K. Its superconductivity is destroyed when the surface magnetic field exceeds 0.100 T. Determine the maximum current a 2.00-mm-diameter niobium wire can carry and remain superconducting, in the absence of any external magnetic field. 9. Serway & Jewett 30.33 A single-turn square loop of wire, 2.00 cm on each edge, carries a clockwise current of 0.200 A. The loop is inside a solenoid, with the plane of the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30 turns/cm and carries a clockwise current of 15.0 A. Find the force on each side of the loop and the torque acting on the


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HARVARD PHYS 11b - Homework #6

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